We analyze the impact of transient and Byzantine faults on the construction of a maximal independent set in a general network. We adapt the self-stabilizing algorithm presented by Turau \cite{turau2007linear} for computing such a vertex set. Our algorithm is self-stabilizing and also works under the more difficult context of arbitrary Byzantine faults. Byzantine nodes can prevent nodes close to them from taking part in the independent set for an arbitrarily long time. We give boundaries to their impact by focusing on the set of all nodes excluding nodes at distance 1 or less of Byzantine nodes, and excluding some of the nodes at distance 2. As far as we know, we present the first algorithm tolerating both transient and Byzantine faults under the fair distributed daemon. We prove that this algorithm converges in $ \mathcal O(\Delta n)$ rounds w.h.p., where $n$ and $\Delta$ are the size and the maximum degree of the network, resp. Additionally, we present a modified version of this algorithm for anonymous systems under the adversarial distributed daemon that converges in $ \mathcal O(n^{2})$ expected number of steps.

翻译：我们分析了瞬时和拜占庭断层对在一般网络中构建最大独立节点的影响。 我们调整了Turau\cite{turau2007linear} 提供的自我稳定算法, 以计算这样的顶点。 我们的算法是自我稳定, 并在任意的拜占庭断层的更困难的背景下运作。 拜占庭节点可以防止与其关系密切的节点参加独立节点, 任意地长期参与。 我们通过侧重于所有节点组合, 排除Byzantine节点1或更远处的节点, 并排除某些节点在距离的自我稳定算法。 据我们所知, 我们提出了第一个在公平分布的守护符下调和拜占庭断层的自我稳定算法。 我们证明, 拜占庭节节节节节节节节节节节点可以防止与其关系密切的节点在 w.h. p. 。 我们给这些节点设定了界限, 美元和 $\ Delta $ 是网络的大小和最大程度, 重调 。